PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
800115852^6061+6061^1585259961Hans Havermann08/2016
800219^46880-2059948Lelio R Paula03/2013
80032^199107-1773759938Enzo Doria05/2013
8004(13*10^59928+83)/359929Robert Price09/2016
800510^59913+10893143159914Marisa Kirisame02/2015
800610^59913+4861959914Patrick De Geest04/2016
800710^59913-7412359913Patrick De Geest03/2016
8008t(199528)59890Robert Price01/2015
80092^198903-1790159876Enzo Doria05/2013
80109*10^59862-1959863Robert Price10/2017
8011gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8012(3^125447+7)/259854Lelio R Paula04/2012
80135^85630+4^(85630-1)59853Robert Price03/2016
80142^198824-213559852Yves Minet06/2013
8015(124^28591-1)/12359851Richard Fischer10/2017
80162^198799-1611759845Enzo Doria04/2013
80177^70811+6^(70811+1)59843Robert Price07/2016
80182^198774-1594559837Enzo Doria04/2013
80192^198753-1587359831Enzo Doria04/2013
8020(31*2^198748-1)/4559829Lelio R Paula01/2014
80212^198725+6959823Lelio R Paula04/2011
8022(68*10^59821+31)/959822Robert Price10/2015
8023(37*25^42785+1867)/859812Curtis Bright05/2015
80243^125354+266059810Lelio R Paula10/2012
8025105^29591-10459810Norbert Schneider08/2013
80264*5^85565-359808Lelio R Paula09/2014
802713963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8029125330^3+3^12533059798Anatoly F. Selevich06/2010
80282^198643-318959798Yves Minet10/2014
8030(13*10^59797+191)/359798Robert Price08/2017
8031(7*10^59796-1)/359797Erik Branger03/2014
80322^198595+15359784Lelio R Paula04/2011
8033(19*10^59766+161)/959767Robert Price07/2016
80342^198510-196559758Lelio R Paula06/2011
80352^198506-1907759757Enzo Doria05/2013
80362^198484-1600559750Enzo Doria04/2013
80372^198473-1682159747Enzo Doria05/2013
8038(2^198481-5)/2831159745Lelio R Paula02/2012
80392^198400-18959725Lelio R Paula04/2011
80402^198384-1283759720Enzo Doria10/2012
804142694!3-72959719Robert Price09/2014
80422^198320-1871759701Enzo Doria05/2013
804320^45881-118359693Enzo Doria03/2013
80442^198224-685559672Lelio R Paula05/2011
80452^198181-1910159659Enzo Doria05/2013
80465*10^59650+4159651Robert Price08/2017
80472^198149-11221359649Enzo Doria06/2014
80482^198138+7369959646Enzo Doria04/2016
80492^198129-5559643Lelio R Paula04/2011
80505^85318-1463659635Enzo Doria02/2013
8051(2^198119+47)/156093559634Lelio R Paula02/2012
80522^198090-1609759632Enzo Doria04/2013
80539*10^59617+8959618Robert Price11/2016
805442625!3+8159612Robert Price09/2014
80555^85277-8459607Lelio R Paula10/2012
8056(871*10^59599-7)/959601Robert Price11/2017
80572^197984-1824559600Enzo Doria05/2013
80582^197951-213759590Yves Minet06/2013
8059(38*10^59589+187)/959590Robert Price11/2017
806066^32749-65^3274959589Robert Price09/2013
80615*10^59586-359587Dmitry Domanov11/2010
8062(35*10^59584-197)/959585Robert Kinser10/2017
80632^197932-395959584Yves Minet04/2017
80642^197909-1896159577Enzo Doria05/2013
8065(3^124871+2)/4503159574Lelio R Paula04/2012
80662^197872+8159566Henri Lifchitz10/2005
80672^197873-1846959566Enzo Doria05/2013
8068(22*10^59558-31)/959559Robert Price04/2015
80702^197840-46559556Lelio R Paula05/2011
8069(31*2^197856-1)/388960559556Lelio R Paula01/2014
80712^197808-1780559547Enzo Doria05/2013
80722^197781-1790559539Enzo Doria05/2013
80732^197777-1747359537Enzo Doria05/2013
80746^76507-14959535Lelio R Paula10/2012
8076Phi(61456,109)59526Enzo Doria05/2012
807518^47420+2359526Lelio R Paula03/2013
8077(59^33613+1)/6059522Paul Bourdelais08/2017
80783^124747+9459520Lelio R Paula10/2012
807917^48370+1859517Lelio R Paula03/2013
808020^45740-152359510Enzo Doria03/2013
8081(47*10^59509+493)/959510Robert Price11/2017
8082(7*2^197642-1)/305159494Lelio R Paula01/2014
808318^47390-185359488Enzo Doria03/2013
8084(2^197581-7)/191559475Lelio R Paula02/2012
8085(24737*2^197559+1)/7759474Lelio R Paula06/2014
80862^197540-245959466Yves Minet07/2014
8087(44*10^59454+1)/959455Serge Batalov11/2010
80882^197494-1780559452Enzo Doria05/2013
80892^197482-1682159449Enzo Doria05/2013
80902^197485+7576759449Enzo Doria04/2016
8091(3*2^197483+1)/2559448Lelio R Paula07/2012
80922^197466-186835159444Enzo Doria04/2016
80932^197411-1778159427Enzo Doria05/2013
8095(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
80942^197392-11462959421Enzo Doria05/2015
80962^197355-15759410Lelio R Paula04/2011
80975^84992-8459407Lelio R Paula10/2012
80982*3^124504-559404Lelio R Paula04/2014
80992^197307-1916559396Enzo Doria05/2013
81002^197303+3276959395Lelio R Paula05/2011
81012*10^59394-6959395Robert Price07/2017
8102(53*10^59389+1)/959390Serge Batalov11/2010
81036^76316-3559386Lelio R Paula10/2012
81042^197259-292959381Yves Minet09/2014
8105lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
810617^48253-659373Lelio R Paula03/2013
81072^197156-1583759350Enzo Doria04/2013
81082^197149-1848159348Enzo Doria05/2013
81092^197142-1715759346Enzo Doria05/2013
8111(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8110(8^65707-5^65707)/359339Robert Price12/2012
8112(2*14283^14283+1)/792549797559334David Broadhurst09/2010
81132^197012-11171959307Enzo Doria05/2014
81142^196975+51359296Lelio R Paula05/2011
8115(61*10^59294+119)/959295Robert Price09/2017
81164*10^59292+3959293Robert Price11/2017
81172^196960+9759291Lelio R Paula04/2011
81189^62116+8^(62116-1)59274Robert Price03/2016
81192^196900-9730559273Lelio R Paula09/2011
81205*6^76155+759261Lelio R Paula09/2014
812115^50385-1459258Wojciech Florek06/2006
8122(136777#-1)/882358147759254Donovan Johnson05/2006
8123(2^196744-3)*6-759227Gilbert Mozzo05/2016
8124(67607*2^196696+1)/359216Lelio R Paula05/2014
81252^196696-11296759212Enzo Doria06/2014
812620^45508-422359208Enzo Doria03/2013
8127gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
812814^51651-8159199Lelio R Paula03/2013
81292^196650-145159198Yves Minet08/2012
81302^196636-279779959194Enzo Doria04/2016
81311111*2^196610-55559189Henri Lifchitz04/2005
81323^124041+65859183Lelio R Paula10/2012
81332^196590-11179759180Enzo Doria05/2014
8134(10^59174-13)/359174Robert Price02/2017
8135(2*10^59174-113)/359174Robert Price09/2017
8136(9179*2^196533-1)/78359164Lelio R Paula04/2015
8137379*10^59152+959155Arkadiusz Wesolowski10/2011
8138(404*10^59149-53)/959151Robert Price11/2017
813913^53095+4059145Lelio R Paula03/2013
81402*F(282999)-159144Henri Lifchitz12/2009
81414*7^69984+359144Lelio R Paula09/2014
8142(5*10^59142+1)/359143Erik Branger12/2013
81432^196463+571159142Lelio R Paula10/2011
81442^196453-9730559139Lelio R Paula09/2011
8145(28*10^59135+53)/959136Serge Batalov11/2008
8146(28*10^59133+113)/359134Robert Price03/2016
81472^196434+759133Lelio R Paula04/2011
8148(8*10^59127-29)/359128Robert Price05/2016
81492^196414+25559127Lelio R Paula05/2011
81505^84586-9259124Lelio R Paula10/2012
81512^196388-1717759119Enzo Doria05/2013
81523^123890+2059111Lelio R Paula10/2012
81532^196355-102177759109Paul Bourdelais11/2012
815411^56754-141059104Enzo Doria11/2012
8155(7*2^196297-1)/120040759087Lelio R Paula01/2014
8156(16*10^59062-19)/359063Robert Price03/2016
815735^38249-122859060Enzo Doria03/2013
81585^84475-1859046Lelio R Paula10/2012
81592^196123-1770159039Enzo Doria05/2013
816012^54702-3159034Lelio R Paula03/2013
81612^196101-17559033Lelio R Paula04/2011
81622^196085+577559028Lelio R Paula05/2011
81632^196034+1171559013Lelio R Paula05/2011
81642^196018-1848559008Enzo Doria05/2013
81652^195984-216358998Yves Minet08/2013
81663^123645-1658994Lelio R Paula10/2012
816739^37078-3858994Norbert Schneider05/2014
81682^195958-1685358990Enzo Doria05/2013
81692^195930-307158981Yves Minet10/2014
81702^195924+51358980Lelio R Paula05/2011
81712^195863+15558961Lelio R Paula04/2011
8172(28*10^58956+113)/358957Robert Price03/2016
817311^56612-930058956Enzo Doria02/2013
81742^195833-1717358952Enzo Doria05/2013
8175(27*2^195833-1)/5358952Lelio R Paula01/2014
8176(13*2^195821-1)/12242558945Lelio R Paula01/2014
8177139^27504-13858942Norbert Schneider10/2015
8178(418*10^58923+23)/958925Robert Price08/2017
81793^123495+4458923Lelio R Paula10/2012
81802^195737-1856558923Enzo Doria05/2013
818114^51407+4758920Lelio R Paula03/2013
81822^195691-9958909Lelio R Paula04/2011
81832^195667-185982758902Enzo Doria04/2016
81852^195642+7549958895Enzo Doria04/2016
8184(299*10^58893+1)/358895Robert Price11/2017
81868*6^75678+558890Lelio R Paula09/2014
81882^195618+7318958887Enzo Doria04/2016
8187(3928^20480+1)/(3928^4096+1)58887Serge Batalov01/2017
8189t(197953)58881Robert Price12/2014
81902^195581-1610558876Enzo Doria04/2013
8191(8*10^58872+67)/358873Robert Price01/2017
81927*2^195542-558865Lelio R Paula03/2014
81932*10^58861+9^5886158862Mike Oakes04/2011
819411^56513-162058853Enzo Doria11/2012
81952^195496+16558851Lelio R Paula04/2011
81965^84187+6658845Lelio R Paula10/2012
8197(28*10^58843-43)/358844Robert Price04/2016
81982^195462-1756558840Enzo Doria05/2013
81992^195449-417158837Yves Minet02/2018
82002^195435+5927358832Yves Minet01/2011
82012^195424-1860558829Enzo Doria05/2013
82022^195385-11158817Lelio R Paula04/2011
82037*10^58815-8358816Robert Price09/2017
8204(47*2^195254+1)/26882158774Lelio R Paula03/2015
82052^195207-1810958764Enzo Doria05/2013
82062^195199-156758761Yves Minet08/2012
82072^195190+7375958759Enzo Doria04/2016
82089*7^69525-458757Lelio R Paula09/2014
82092^195170-1804558753Enzo Doria05/2013
82102^195166-16558751Lelio R Paula04/2011
8211(754*10^58748-7)/958750Robert Price11/2017
8212(22699*2^195140+1)/17558746Lelio R Paula05/2014
82137*3^123109-258739Lelio R Paula04/2014
8214(8*10^58738-611)/958738Robert Price11/2017
821518^46790+7758735Lelio R Paula03/2013
82172^195095-33729758730Gary Barnes09/2009
8216(14*10^58729+31)/958730Robert Price02/2015
821899^29424+9858720Norbert Schneider07/2013
8219(15185*2^195039-1)/21958715Lelio R Paula04/2015
82202^195001-6958702Lelio R Paula04/2011
82212^194978-48781158695Gary Barnes09/2009
8222163^26530+26530^16358690Serge Batalov05/2014
82232^194940-194940+158683Robert Price10/2014
8224(76*10^58669+41)/958670Robert Price10/2015
822514^51186+8758666Lelio R Paula03/2013
82262^194878-9730558665Lelio R Paula09/2011
82275^83927-1813658663Enzo Doria05/2014
8228(24737*2^194865+1)/108558662Lelio R Paula06/2014
82297^69411+4058660Lelio R Paula10/2012
82306^75382-7958659Lelio R Paula10/2012
82312^194854+2758657Lelio R Paula04/2011
82322^194801+2983558641Lelio R Paula10/2012
82332^194752+19558627Lelio R Paula04/2011
82347^69371-6^6937158626Predrag Minovic08/2004
82352^194747-11251958625Enzo Doria06/2014
8236(15*2^194737+1)/5958622Lelio R Paula07/2012
8237(23*2^194700+1)/358612Lelio R Paula02/2012
823810^58608+5527358609Patrick De Geest07/2017
823910^58608-80000158608Robert Price06/2017
824010^58608-6011958608Patrick De Geest07/2017
82415^83836+7658599Lelio R Paula10/2012
824218^46664+3158577Lelio R Paula03/2013
8243(34*10^58577-7)/9/19/46358574Makoto Morimoto04/2016
82442^194574+16558573Lelio R Paula04/2011
82452^194569-1221158572Enzo Doria06/2014
824610^58571+5^58571+2^5857158572Robert Price12/2016
824710^58571+20283758572Patrick De Geest02/2017
8248(10^58571+41)/358571Robert Price01/2017
824910^58571-34362958571Patrick De Geest02/2017
8250(43*10^58563-403)/958564Robert Price04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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